An Efficient Computational Technique for Fractional Brusselator Reaction–Diffusion Equations

Abstract

This paper investigates the fractional Brusselator reaction–diffusion equation with Caputo derivative by using a novel computational approach, the Laplace iterative method which integrates the Laplace transform and the Gejji-Jafari iterative method. The existence and uniqueness of the solutions are examined. The study presents two examples demonstrating the method’s capability to produce accurate numerical solutions with low error values, illustrated through comprehensive numerical analysis and graphical representations. The numerical results are compared with existing methods and exact solutions using three metrics: Root Mean Square, \({L}^{2},\) and \({L}^{\infty }\) error norms. Additionally, consecutive errors are calculated to further validate the method's accuracy and reliability. Our findings indicate that the proposed method is a robust and efficient approach for solving the fractional Brusselator reaction–diffusion equation, contributing to the advancement of numerical methods in fractional calculus and reaction–diffusion modelling.